SAMPLING LOCALIZATION AND DUALITY ALGORITHMS IN PRACTICE

In a recent paper, Anderssen and Davies [Simple moving-average formula e for direct recovery of the relaxation spectrum, Mathematics Research Report MRR 016-98, Centre for Mathematics and its Applications, The A ustralian National University] have derived moving-average formulae wh ich can be applied to oscillatory shear data to recover estimates of t he relaxation spectrum of the viscoelastic material tested. These movi ng-average formulae represent an improvement over commercial packages currently available, for two reasons. First, they take the limits impo sed by sampling localization in determining the relaxation spectrum fu lly into account. Secondly, to within finite resolution, these formula e yield accurate relaxation spectra in a fraction of a second on a PC. Anderssen and Davies have also indicated that their formulae are best employed within an iterative algorithm which exploits the natural dua lity between storage and loss moduli. The purpose of this paper is to pursue this natural duality further, and present a class of fast algor ithm accessible to the experimentalist. Their performance when applied to noisy data is described. Their success is attributed to the implic it duality constraints imposed through sampling localization and the K ramers-Kronig relations, and to the nature of the regularization impos ed. (C) 1998 Elsevier Science B.V. All rights reserved.